Divide -3x^3 - 2x^2 - x - 2 by x – 2.


A. -3x2 - 8x - 17, R –36
B. -3x2 + 4x + 15, R 32
C. -3x2 + 4x + 15
D. -3x2 - 8x - 17

I'm sure it's either B or C, can someone help?

What made you "sure" it was B or C ?

Did you perform a long algebraic or synthetic division??

sorry, I meant A or B, because I am "sure" that there is a remainder from looking at the equation. I just needed someone to help go through the equation.

To divide -3x^3 - 2x^2 - x - 2 by x - 2, you can use long division. Here's how you can do it step by step:

Step 1: Write the expression in descending order of powers:
-3x^3 - 2x^2 - x - 2

Step 2: Divide the first term of the dividend (-3x^3) by the first term of the divisor (x). The result is -3x^2. Write this above the line.

___________
x - 2 | -3x^3 - 2x^2 - x - 2
-3x^3 + 6x^2

Step 3: Multiply the result (-3x^2) by the divisor (x - 2) and write the product under the dividend. Then, subtract it from the dividend.

___________
x - 2 | -3x^3 - 2x^2 - x - 2
-3x^3 + 6x^2
___________
- 8x^2 - x - 2

Step 4: Bring down the next term from the dividend (-8x^2).

___________
x - 2 | -3x^3 - 2x^2 - x - 2
-3x^3 + 6x^2
___________
- 8x^2 - x - 2
- 8x^2 + 16x

Step 5: Repeat steps 2 to 4 until you have no more terms in the dividend.

___________
x - 2 | -3x^3 - 2x^2 - x - 2
-3x^3 + 6x^2
___________
- 8x^2 - x - 2
- 8x^2 + 16x
___________
15x - 2

Step 6: Since the degree of the remainder (15x - 2) is less than the degree of the divisor (x - 2), the division is complete.

In the options provided, the correct answer is C. -3x^2 + 4x + 15.
The remainder is 15x - 2, which is not equal to either R - 36 or R 32 as mentioned in the options A and B.